Find lim   x3 + 3x2 + 3x + 1      x - 1    2x3 + 3x2 - 1

Q: A post 20 meters long stands vertically in a horizontal plane. Another post stands vertically on the...

A: Given: A post 20 meters long stands vertically in a horizontal plane. Another post 45 meters high st...

Q: Let R be the region inside the polar curve r = 2 sin 0 and outside the polar curve r = 3 – 2 sin 0 a...

A:

Q: A function y(t) satisfies the differential equation dy =y4-5y3+ 6y2. dt (a) What are the constant so...

A:

Q: 4. Use the method of undetermined coefficients to find a particular solution to the system below. Pr...

A:

Q: Find dy/dx for: y = x2 − sec x + 1

A:

Q: The functions represent the position of a particle traveling along a horizontal line, s(t) = 3t3 − 2...

A: for time t,t≥0 s(t)=3t3-20t2+48 t -20V(t) =dsdt =ddt(3t3-20t2+48 t -20)V(t) = 9 t2-40 t+48v(t)>0 ...

Q: Find the limits of the functions below a) limr-3 x* sin x b) lim,

A:

Q: Let f(x) = 2x° + 20x + 3. a. Find the values of x for which the slope of the curve y=f(x) is 0. b. F...

A:

Q: Case 4: repeated quadratic factor (very hard!) 8dx • Example 1: r(r2+2)2

A: To evaluate: I=∫8 dxx(x2+2)2 Substitute x2+2=u⇒2x dx=du⇒dx=12xdu So, I=∫8 x(u2)du2x=4∫1x2u2du=4∫1(u-...

Q: u = (5, 5) v = (7, 1) %3D

A: Given : u=<5, 5> v=<7, 1>

Q: If Ax) = x² + 3x – 2 and g(x) = X+2 then g(f(-1)) is equal to 6.

A: The objective of the question is evaluate the value at the given functions of composition.

Q: A given partial fraction 2x A B Cx +D (x- 1)(x+ 4)(x²+ 1) + X+4 X-a x² +1 B can be evaluated as: O 8...

A:

Q: Q3) Find the volume of the solid generated by revolving region bounded by the curve (y-e*) & the lin...

A: Integral

Q: Question 4 x³dx (x²+2) ³ 1 A 2(x²+2) ' 2(x²+2) ? 1 1 В 2(x²+2) 2(x²+2) ² 1 +C 4(x²+2) ' 2(x²+ 2) 2 D...

A: Here, the given integral is: I=∫x3(x2+2)3dx⇒I=∫x2x(x2+2)3dx...(1)

Q: Find the indefinite integral. X COS 9TX

A: Given,I=∫ xcos9πx2dxPut u=9πx2Differentiatedu=9π(2x)dxdu=18πxdxdu18π=xdxThereforeI=∫xcos9πx2dxI=∫cos...

Q: J. E n=1 Vn 2.

A: p-test series for a series to be convergence ∑n=1∞1np will diverge if p≤1              will converge...

Q: Parametrize the following two curves in R3 and find their arclength. (1) the intersection of the cyl...

A: Since, you have posted multiple questions, as per guidelines we will solve only first question. If y...

Q: 5x Determine the values of x for which the function f (x) = is discontinuous. x2+x

A:

Q: Determine the real number ? such that vectors a = 3i + 2j and b = 6i + ?j are orthogonal.

A:

Q: Graph the integrand and use known area formulas to evaluate the integral: dx

A:

Q: Use logarithmic differentiation to find the derivative of the function. y = x4/x y'(x) =

A:

Q: h(x) = x2 – 4. Is h1 a function and why/why not? %3D No, the inverse function does not pass the vert...

A:

Q: Differentiate the function. y = In(e-X + xe¬X) y' = II

A:

Q: Solve using alternating series

A:

Q: Use sigma notation to write the Taylor series about x = xo for the function. e*; xo = 4 %3D k! k=0 4...

A: Taylor's series about x=x0 for the function ex; x0=4

Q: grocery

A: Please refer to the image below

Q: Q1 Choose only two: A) Solve the inequalities and show the solution sete B) Solve the equation: 18 –...

A: In this question we will use basic concepts of inequality. Solution of the above question is in the ...

Q: What is the equation of the tangent line to the curve y = x2 – 2x + 1 at point (3,4)? a. y = -4x + 8...

A: as per guidelines I can only do first 3 subparts

Q: مرمع الراشرة

A:

Q: Use Stokes’ Theorem to evaluate the closed loop line integral F*dr where F(x,y,z) = xi + yj + 3(x^2+...

A:

Q: 1. A movie theater seats 240 people. For any particular show, the amount of money the theater makes ...

A: According to question,Given,Number of people n= 240 - 12pwhere,p is the price of one tickets. 

Q: What integration technique can be used to integrate: sec3 xdx Integration Formulas O Trigonometric S...

A:

Q: 30 Choose the best answer: tan x + cot x =

A: Given

Q: To integrate v3 x2dy we apply integration by parts and in the form u dv, u is set as: 2 of 11

A:

Q: Which of the following functions have a 4th derivative different from itself? ex sin x CoS X

A: In this question, we need to find which of the given functions have a 4th derivative different from ...

Q: dx 2- Find dy of y = /cos-1(In (xy)) y %3D

A: Given: - The function is, y=cos-1(ln(xy))xy To find: - The derivative of the function, dxdy

Q: Find if converging or diverging using nth term test

A: ∑n=1∞-1nn5    an = -1nn5    We can now proceed with nth term test.. 

Q: A given partial fraction Cx +D x² +1 2x A + X+4 (x-1)(x+4)(x² +1) X-a A can be evaluated as: O 15 2/...

A: Given that partial fraction 2xx-1x+4x2+1=Ax-1+Bx+4+Cx+Dx2+1To find : value of ASolution:2xx-1x+4x2+1...

Q: A population is modeled by the differential equation 1.20(1 -) dP dt 4300 (a) For what values of P i...

A: Given :dPdt=1.2P1-P4300

Q: |(3x² +2)' {x) = x*(4x – 1)

A:

Q: Given the function y=f(x), y' is found to be negative over the interval (4,8), then over this interv...

A:

Q: Graph the integrand and use known area formulas to evaluate the integral: dx

A:

Q: Given the series 3" Σ n=1 antl find the ratio an (Express numbers in exact form. Use symbolic notati...

A:

Q: Let be the function with first derivative g'(x) = Vx3 + x for x > 0. If g(2) = -7, what is the value...

A:

Q: Which of the following statements is TRUE? (Circle ALL that apply) a. A constant function has no der...

A: answer is D a polynomial function is always differentiable. this is the property of simple function ...

Q: Match each range of angles with each inverse trig function. acrsin x csc arccos x sec-x cot 1x: arct...

A: Here we will see the correct range of each inverse trig. function,

Q: For the function y =f(x), it was found out that f(c) = 0. What can be said that x=c ? critical point...

A: topic - functions

Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = x0 and then find the nth Taylo...

A:

Q: Write the first five terms of the recursively defined sequence. a1 =6, ak+ 1 %3D %3D a2 = 23 = a4 a5...

A:

Q: u³ = a²t , find d’u %3D dt3 2a4 а. 9u5 10a6 27u8 -10a6 С. Zu® 40a6 d. U8 b.

A: A detailed solution is given below